Say I irreversibly deleted my camera in my scene. Could I solve for its position, given a prior 2d render of the scene?
Well you can import the previous render as a reference image and add a new camera, flatten them both out using (ctrl+R and then ctrl+G), then hop inside of your camera and raise it above your image until it fills out the camera borders correctly, and then lastly parent the image to the camera and turn down it's opacity.

All you would need to do from there is fly around a bit with shift+` and find your previous location. It would basically serve as an overlay guide to help you find your old position.